A weighted inverse minimum s – t cut problem with value constraint under the bottleneck-type Hamming distance

Abstract

Given a network G = (N, A, c) and an s − t cut [S, ¯ S] with the capacity β and the constant value α, an inverse minimum s − t cut problem with value constraint is to modify the vector capacity c as little as possible to make the s − t cut [S, ¯ S] become a minimum s−t cut with the capacity α. The distinctive feature of this problem with the inverse minimum cut problems is the addition of a constraint in which the capacity of the given cut has to equal to the preassumed value α. In this article, we investigate the inverse minimum s−t cut problem with value constraint under the bottleneck weighted Hamming distance. We propose two strongly polynomial time algorithms based on a binary search to solve the problem. At each iteration of the first one, we solve a feasible flow problem. The second algorithm considers the problem in two cases β > α and β < α. In this algorithm, we first modify the capacity vector such that the given cut becomes a minimum s − t cut in the network and then, by preserving optimality this s − t cut, adjust it to satisfy value constraint.